Science:Math Exam Resources/Courses/MATH100/December 2010/Question 01 (e)/Hint 2

To help us out we should break the problem down into smaller subproblems. Let $f_{1}(x)=x^{5}$ and let $f_{2}(x)=\sin(\cos(3x^{2}))$. Then $y=f_{1}(f_{2}(x))=\sin ^{5}(\cos(3x^{2}))$. So the derivative by the chain rule is

$\displaystyle y'=f'_{1}(f_{2}(x))f_{2}'(x)$

To solve for the derivative of $f_{2}(x)$ we again use the chain rule...